Discrete Mathematics with Algorithms

This is a first-year course in discrete mathematics requireing no calculus or computer programming experience.

The approach stresses finding efficient algorithms, rather than existential results. Provides an introduction to constructing proofs (especially by induction), and an introduction to algorithmic problem-solving. All algorithms are presented in English, in a format compatible with the Pascal programming language. Contains many exercises, with answers at the back of the book (detailed solutions being supplied for difficult problems).

Title Discrete Mathematics with Algorithms
Author(s) M. O. Albertson and J. P. Hutchinson
Publisher: John Wiley & Sons; 1st Updated edition (July 22, 1988)
Hardcover 560 pages
Language: English
ISBN-10/ASIN: 0471849022
ISBN-13: 978-0471849025
eBook: http://www.macalester.edu/~hutchinson/book/book.html

Book of Proof, 2nd Edtion

This book is an introduction to the language and standard proof methods of mathematics.

It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

Title Book of Proof, 2nd Edtion
Author(s) Richard Heath Hammack
Publisher: Richard Hammack; Revised edition (May 31, 2013)
Paperback 312 pages
Language: English
ISBN-10: 0989472108
ISBN-13: 978-0989472104
eBook: http://www.people.vcu.edu/~rhammack/BookOfProof/

Discrete Mathematics for Computer Science

This book gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given.

With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics.

There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem.

We also discuss matchings, covering, bipartite graphs.

The book is highly illustrated and each chapter ends with a list of problems of varying difficulty. Undergraduates in mathematics and computer science will find this book useful.

Title Discrete Mathematics for Computer Science
Author(s) Jean Gallier
Publisher: Springer; 2011 edition (January 25, 2011)
Hardcover/Paperback 477 pages
Language: English
ASIN: 1441980466
ISBN-13: 978-1441980465
Download: http://arxiv.org/pdf/0805.0585v1.pdf

Exploring Discrete Mathematics With Maple

This is the first supplement in discrete mathematics to concentrate on the computational aspects of the computer algebra system Maple. Detailed instructions for the use of Maple are included in an introductory chapter and in each subsequent chapter.

Each chapter includes discussion of selected Computational and Exploration exercises in the corresponding chapter of Ken Rosen's text Discrete Math and It's Applications, Third Edition. New exercises and projects are included in each chapter to encourage further exploration of discrete mathematics using Maple. All of the Maple code in this supplement is available online via the Waterloo Maple Web site, in addition to new Maple routines that have been created which extend the current capabilities of Maple.

Title Exploring Discrete Mathematics With Maple
Author(s) Kenneth H. Rosen
Publisher: Mcgraw-Hill College; 4th edition (August 1, 1996)
Paperback 400 pages
Language: English
ISBN-10: 0070541280
ISBN-13: 978-0070541283
Download: http://highered.mcgraw-hill.com/sites/0073383090/student_view0/exploring_discrete_mathematics_using_maple.html

Applied Discrete Structures

Applied Discrete Structures is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces.

Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative.

Title Applied Discrete Structures
Author(s) Al Doerr, Ken Levasseur
Publisher: John Wiley & Sons; 1st Updated edition (July 22, 1988)
Hardcover/Paperback 496 pages
eBook PDF files
Language: English
ISBN-10/ASIN: 1105559297
ISBN-13: 978-1105559297
Download Link: http://faculty.uml.edu/klevasseur/ads2/